Fluid Mechanics for Chemical Engineering

Chapter 14

Flows in Porous Media

This chapter deals with the physical principles that govern flows in porous media. Such flows have a wide range of applications in oil extraction, civil engineering and geomechanics (mechanical behavior of soils), or in hydrogeology (water resources). In the process field, filtration is widely used in the agri-food and environment industries (water treatment, dust removal, etc.).

Having introduced in the first section the characteristic parameters of the geometrical structure of a porous medium, we establish Darcy’s law, which links the flux through a porous medium to the pressure gradient that is applied. The characteristic hydrodynamic parameter of a porous medium is its permeability. In section 14.5, we establish the Kozeny–Carman formula, which models permeability according to the geometrical parameters of the porous medium. Darcy’s model is extended in section 14.6 to the turbulent regime, introducing Ergun’s relation, which describes the flow in highly permeable porous media. Applications treated more directly in this chapter are the filtration processes. We introduce the notion of membrane resistance to filtration and discuss the case of filtration by pressing (section 14.7), whereby by compressing the porous medium, the liquid held inside the porous medium gets drained. That process couples the flow in the porous medium to the mechanical behaviour of the solid skeleton constituting the porous medium.

Membrane separation processes are not ...